Question

1. If a researcher wants to examine the relationship among variables and not the difference, what test statistics should he or she use? Please provide an example.

2. What about significance versus meaningfulness? What should you keep in mind? Please provide an example.

Answer 1

Example we want to check how price of a hosue is related to size and bath rooms

data is

Price	size	bathrooms
260.9	2666	2.5
337.3	3418	3.5
268.4	2945	2
242.2	2942	2.5
255.2	2798	3
205.7	2210	2.5
249.5	2209	2
193.6	2465	2.5
242.7	2955	2
244.5	2722	2.5

Dependent variable is Y=Price

Indpendent variables is X=size and Bathrooms

let us try to fit a regression in excel

we get

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.784579
R Square	0.615565
Adjusted R Square	0.505726
Standard Error	27.12153
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	2	8244.737	4122.368	5.604261	0.035227
Residual	7	5149.043	735.5776
Total	9	13393.78
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	19.19286	69.55308	0.275946	0.790559	-145.274	183.6598
size	0.070262	0.027897	2.518636	0.03989	0.004296	0.136227
bathrooms	15.51271	21.92956	0.707388	0.50219	-36.3425	67.36787

From output

Regression equation is

Price=19.19286+0.070262*size+15.51271*bathrooms

we want to check overall regression model is significant or not ,Then we use Global F test

Look for F and p values

For Global F test

Ho:

Ha:atleast one of the

F=5.604261

p=0.035227

say alpha=0.05

p<0.05

Reject Ho

Accept Ha

Conclude that atlest one of the beta is signifcant

we can use this model for predicting price from szie and bathrooms

If we want to check whether indpendent variables are significant variables or not look for t an d p values

From above output:

	Coefficients	Standard Error	t Stat	P-value
Intercept	19.19286	69.55308	0.275946	0.790559
size	0.070262	0.027897	2.518636	0.03989
bathrooms	15.51271	21.92956	0.707388	0.50219

For size ,t=2.518 p=0.03989,p<0.05,size is significant variable in predicting price

For bathrooms,t=21.929,p=0.7074,p>0.05,bathrooms is not a significant variable in predicting price